<h2>Problem 233</h2>
<div style="color:#666;font-size:80%;">20 February 2009</div><br />
<div class="problem_content">
<p>Let <var>f</var>(<var>N</var>) be the number of points with integer coordinates that are on a circle passing through (0,0), (<var>N</var>,0),(0,<var>N</var>), and (<var>N</var>,<var>N</var>).</p>
<p>It can be shown that <var>f</var>(10000)&thinsp;=&thinsp;36.</p>

<p>What is the sum of all positive integers <var>N</var>&thinsp;<img src='images/symbol_le.gif' width='10' height='12' alt='&le;' border='0' style='vertical-align:middle;' />&thinsp;10<img src="" style="display:none;" alt="^(" /><sup>11</sup><img src="" style="display:none;" alt=")" /> such that <var>f</var>(<var>N</var>)&thinsp;=&thinsp;420&thinsp;?</p>
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